The homeless man was lying on the ground, shaking, when police arrived early Wednesday. His face was soaked, apparently with urine, his nose broken, his chest and arms battered.

Police said two brothers from South Boston ambushed the 58-year-old as he slept outside of a Dorchester MBTA stop, and targeted him because he is Hispanic. One of the brothers said he was inspired in part by GOP presidential candidate Donald Trump.

The allegations ignited widespread condemnation Wednesday.

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Mayor Martin J. Walsh said the brothers “should be ashamed of themselves.” Boston’s top prosecutor, Daniel F. Conley, called the case “sickening.”

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Police Commissioner William B. Evans, a South Boston resident, said the brothers had given his neighborhood “a bad name.” He called it “a disgrace.”

Trump, told of the alleged assault, said “it would be a shame . . . I will say that people who are following me are very passionate. They love this country and they want this country to be great again. They are passionate.”

Trump, in his campaign kickoff speech in June, made disparaging comments about Mexican immigrants that advocates feared could cause a backlash against immigrants.

In Dorchester District Court on Wednesday, Scott and Steve Leader, who have extensive criminal records, pleaded not guilty to multiple assault charges with a dangerous weapon, indecent exposure, and making threats. The men stayed behind a half-open door during their court hearing to avoid cameras; their lawyers declined to comment on the charges against them.

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Steve Leader is also charged with malicious destruction of property over $250 after he allegedly punched and kicked a cell door at the State Police barracks in South Boston.

Judge Lisa A. Grant ordered the men held without bail.

During the proceedings, Suffolk Assistant District Attorney Andrew Kettlewell described the attack as “vicious and unprovoked.”

According to State Police, the Leader brothers were on their way home from a Red Sox game when they found the victim sleeping near the John F. Kennedy/UMass stop on the Red Line.

He told police he was awakened by two men urinating on his face. He said they ripped away his blankets and sleeping bag, and started rummaging through his things.

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“Next thing . . . he was getting hit in the face and head,” according to the State Police report. “He remembers being punched several times and hit with the metal pole.”

The man was taken to Boston Medical Center, where he remained in fair condition Wednesday afternoon, a hospital spokeswoman said. The police report said he had a broken nose, bruises on his head, and a large bruise across his torso.

The brothers walked away from the scene laughing, a witness told State Police.

Alerted by witnesses, troopers arrested the brothers, and said the men continued to be disorderly in custody. Steve Leader allegedly urinated on his cell door, and both brothers allegedly made threats to staff members.

Police said Scott Leader, 38, told them it was OK to assault the man because he was Hispanic and homeless.

“Donald Trump was right, all these illegals need to be deported,” he allegedly told the police.

Scott Leader also told police that the homeless man had started the confrontation by attacking his brother Steve, 30, with the pole.

Witnesses told police they saw the men attack the homeless man. One woman said she saw him hunched over and clutching the pole, apparently to defend himself, according to the report. She told police one of the suspects grabbed the pole and struck him three or four times, including in the head.

Prosecutors and police said the Leader brothers have extensive criminal records.

Scott Leader was convicted of a hate crime and imprisoned for one year after attacking a Moroccan man in Boston days after the Sept. 11, 2001, terror attacks, according to court records. Leader threw a cup at the man, who was working at a Dunkin’ Donuts, calling him “terrorist” and several ethnic slurs.

Similar attacks have flared up in Massachusetts and elsewhere in the nation, often after immigrants are in the news.

“Every time that immigrants are being scapegoated or targeted, something happens,” said Eva Millona, executive director of the Massachusetts Immigrant and Refugee Advocacy Coalition, an umbrella group of organizations in the state.

News of the Boston attack emerged on the same day that advocates for immigrants held a rally at the State House to urge Governor Charlie Baker, a Republican, to meet with them to discuss immigrant rights. After they waited several hours, Baker agreed to set a meeting.

Patricia Montes, executive director of Centro Presente, an East Boston nonprofit that organized the rally, said she hoped to steer the conversation away from the invective that has characterized Trump’s campaign for the Republican presidential nomination.

In his campaign kickoff speech in June, Trump suggested that most Mexican immigrants are criminals, saying they are “bringing drugs. They’re bringing crime. They’re rapists. And some, I assume, are good people.”

The speech ignited outrage and spurred Univision, NBC, Macy’s, and others to cut ties with Trump.